The Senate put the legislation aside because the proposal to expand the FBI’s system of processing purchasers lacked the 60 votes needed to advance.

In September, Dublin-based Accenture won a 41/2-year FBI contract worth as much as $32 million to update and expand the information technology system used to vet buyers. Accenture also is one of the contractors eligible to supply the FBI with IT products and services as part of an eight-year blanket contract awarded in 2010 and valued at as much as $30 billion.

The September agreement “will help the FBI handle an increase in gun purchases efficiently,” Joanne Veto, an Accenture spokeswoman, said by e-mail.

Computer Sciences, based in Falls Church, operates an FBI call center in West Virginia that processes gun-dealer inquiries under a contract estimated at as much as $59 million when it was issued in 2009. A new contract for that call center, with an estimated value between $50 million and $100 million, could be awarded by Sept. 30, according to a forecast by the Justice Department.

Shares of Accenture and Computer Sciences have been trading higher since the beginning of the year, even as both companies cited the automatic federal spending cuts known as sequestration as a potential risk that could limit new government contracts or reduce payments under existing accords. About 10 percent of Computer Science’s revenue came from civilian public agencies in its fiscal year ended March 30. About 10 percent of Accenture’s operating income came from government work in its fiscal year ending Aug. 31.

In addition to Accenture and Computer Sciences, McLean-based SAIC and two Fairfax-based companies, ManTech International and SRA International, have been awarded contracts to provide vetting-system services.

The Obama administration estimated in its budget request that expanding background checks to all private firearms sales would have doubled the system’s workload. The administration projected that if such a universal requirement was imposed, the FBI would need to spend $168 million in fiscal 2014, or $100 million more than projected under current law.

In 2012, the government received about 19.6 million background-check requests, according to an FBI report.

“The system is maxed out,” said Mike Bazinet, a spokesman for the Newtown, Conn.-based National Shooting Sports Foundation, a trade group that represents firearms manufacturers and retailers and opposes expanding background checks. “Any additional requirements of the system, unless it was to get more resources, they may not be able to handle that.”

In the last two months of 2012 — the peak period for holiday and hunting-season gun sales — the FBI fell short of its goals for responding to background-check inquiries, according to a bureau report. Calls to vet gun buyers took more than four minutes to answer, on average, during December, compared with a target of nine seconds or less.

Earlier, the FBI said its system was hampered by outdated technology and inconsistent databases, and wrote that it could not handle expanding gun sales or any new obligations.

“Performance gaps would have an effect on how the NICS can make necessary changes to meet any new legislation,” according to an FBI document referring to the National Instant Criminal Background Check System last updated in July.

The measure that stalled in the Senate also sought faster processing of vetting requests, putting more demands on the FBI’s system.

Current law makes gun buyers wait as long as three days for a response from the FBI. The stalled legislation sought to reduce that wait to 48 hours after two years and 24 hours after four years.

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